Efficient advanced encryption standard implementation using lookup and normal basis

A new type of advanced encryption standard (AES) implementation using a normal basis is presented. The method is based on a lookup technique that makes use of inversion and shift registers, which leads to a smaller size of lookup for the S-box than its corresponding implementations. The reduction in the lookup size is based on grouping sets of inverses into conjugate sets which in turn leads to a reduction in the number of lookup values. The above technique is implemented in a regular AES architecture using register files, which requires less interconnect and area and is suitable for security applications. The results of the implementation are competitive in throughput and area compared with the corresponding solutions in a polynomial basis.

Double complexes and vanishing of Novikov cohomology

We consider non-standard totalisation functors for double complexes, involving left or right truncated products. We show how properties of these imply that the algebraic mapping torus of a self map h of a cochain complex of finitely presented modules has trivial negative Novikov cohomology, and has trivial positive Novikov cohomology provided h is a quasi-isomorphism. As an application we obtain a new and transparent proof that a finitely dominated cochain complex over a Laurent polynomial ring has trivial (positive and negative) Novikov cohomology.

Detecting Deception in Movement: The Case of the Side-Step in Rugby

Although coordinated patterns of body movement can be used to communicate action intention, they can also be used to deceive. Often known as deceptive movements, these unpredictable patterns of body movement can give a competitive advantage to an attacker when trying to outwit a defender. In this particular study, we immersed novice and expert rugby players in an interactive virtual rugby environment to understand how the dynamics of deceptive body movement influence a defending player’s decisions about how and when to act. When asked to judge final running direction, expert players who were found to tune into prospective tau-based information specified in the dynamics of ‘honest’ movement signals (Centre of Mass), performed significantly better than novices who tuned into the dynamics of ‘deceptive’ movement signals (upper trunk yaw and out-foot placement) (p<.001). These findings were further corroborated in a second experiment where players were able to move as if to intercept or ‘tackle’ the virtual attacker. An analysis of action responses showed that experts waited significantly longer before initiating movement (p<.001). By waiting longer and picking up more information that would inform about future running direction these experts made significantly fewer errors (p<.05). In this paper we not only present a mathematical model that describes how deception in body-based movement is detected, but we also show how perceptual expertise is manifested in action expertise. We conclude that being able to tune into the ‘honest’ information specifying true running action intention gives a strong competitive advantage.

Model categories for orthogonal calculus

We restate the notion of orthogonal calculus in terms of model categories. This provides a cleaner set of results and makes the role of O(n)-equivariance clearer. Thus we develop model structures for the category of n-polynomial and n-homogeneous functors, along with Quillen pairs relating them. We then classify n-homogeneous functors, via a zig-zag of Quillen equivalences, in terms of spectra with an O(n)-action. This improves upon the classification theorem of Weiss. As an application, we develop a variant of orthogonal calculus by replacing topological spaces with orthogonal spectra.

On the Condition Number Distribution of Complex Wishart Matrices

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading. © 2010 IEEE.

A Wavelet Approach to the Selective Computation of Eigenvalues for Small Signal Stability Analysis

This paper proposes a method to assess the small signal stability of a power system network by selective determination of the modal eigenvalues. This uses an accelerating polynomial transform, designed using approximate eigenvalues
obtained from a wavelet approximation. Application to the IEEE 14 bus network model produced computational savings of 20%,over the QR algorithm.

Algorithms for Self-Healing Networks

Many modern networks are \emph{reconfigurable}, in the sense that the topology of the network can be changed by the nodes in the network. For example, peer-to-peer, wireless and ad-hoc networks are reconfigurable. More generally, many social networks, such as a company's organizational chart; infrastructure networks, such as an airline's transportation network; and biological networks, such as the human brain, are also reconfigurable. Modern reconfigurable networks have a complexity unprecedented in the history of engineering, resembling more a dynamic and evolving living animal rather than a structure of steel designed from a blueprint. Unfortunately, our mathematical and algorithmic tools have not yet developed enough to handle this complexity and fully exploit the flexibility of these networks. We believe that it is no longer possible to build networks that are scalable and never have node failures. Instead, these networks should be able to admit small, and maybe, periodic failures and still recover like skin heals from a cut. This process, where the network can recover itself by maintaining key invariants in response to attack by a powerful adversary is what we call \emph{self-healing}. Here, we present several fast and provably good distributed algorithms for self-healing in reconfigurable dynamic networks. Each of these algorithms have different properties, a different set of gaurantees and limitations. We also discuss future directions and theoretical questions we would like to answer. %in the final dissertation that this document is proposed to lead to.

Self-healing systems and virtual structures

Modern networks are large, highly complex and dynamic. Add to that the mobility of the agents comprising many of these networks. It is difficult or even impossible for such systems to be managed centrally in an efficient manner. It is imperative for such systems to attain a degree of self-management. Self-healing i.e. the capability of a system in a good state to recover to another good state in face of an attack, is desirable for such systems. In this paper, we discuss the self-healing model for dynamic reconfigurable systems. In this model, an omniscient adversary inserts or deletes nodes from a network and the algorithm responds by adding a limited number of edges in order to maintain invariants of the network. We look at some of the results in this model and argue for their applicability and further extensions of the results and the model. We also look at some of the techniques we have used in our earlier work, in particular, we look at the idea of maintaining virtual graphs mapped over the existing network and assert that this may be a useful technique to use in many problem domains.

Hexavalent Chromium Adsorption by a Novel Activated Carbon Prepared by Microwave Activation

Microwave heating reduces the preparation time and improves the adsorption quality of activated carbon. In this study, activated carbon was prepared by impregnation of palm kernel fiber with phosphoric acid followed by microwave activation. Three different types of activated carbon were prepared, having high surface areas of 872 m2 g-1, 1256 m2 g-1, and 952 m2 g-1 and pore volumes of 0.598 cc g-1, 1.010 cc g-1, and 0.778 cc g-1, respectively. The combined effects of the different process parameters, such as the initial adsorbate concentration, pH, and temperature, on adsorption efficiency were explored with the help of Box-Behnken design for response surface methodology (RSM). The adsorption rate could be expressed by a polynomial equation as the function of the independent variables. The hexavalent chromium adsorption rate was found to be 19.1 mg g-1 at the optimized conditions of the process parameters, i.e., initial concentration of 60 mg L-1, pH of 3, and operating temperature of 50 oC. Adsorption of Cr(VI) by the prepared activated carbon was spontaneous and followed second-order kinetics. The adsorption mechanism can be described by the Freundlich Isotherm model. The prepared activated carbon has demonstrated comparable performance to other available activated carbons for the adsorption of Cr(VI).

A multi-output two-stage locally regularized model construction method using the extreme learning machine

This paper investigates the construction of linear-in-the-parameters (LITP) models for multi-output regression problems. Most existing stepwise forward algorithms choose the regressor terms one by one, each time maximizing the model error reduction ratio. The drawback is that such procedures cannot guarantee a sparse model, especially under highly noisy learning conditions. The main objective of this paper is to improve the sparsity and generalization capability of a model for multi-output regression problems, while reducing the computational complexity. This is achieved by proposing a novel multi-output two-stage locally regularized model construction (MTLRMC) method using the extreme learning machine (ELM). In this new algorithm, the nonlinear parameters in each term, such as the width of the Gaussian function and the power of a polynomial term, are firstly determined by the ELM. An initial multi-output LITP model is then generated according to the termination criteria in the first stage. The significance of each selected regressor is checked and the insignificant ones are replaced at the second stage. The proposed method can produce an optimized compact model by using the regularized parameters. Further, to reduce the computational complexity, a proper regression context is used to allow fast implementation of the proposed method. Simulation results confirm the effectiveness of the proposed technique. © 2013 Elsevier B.V.

The Influence of Structural Modeshape Variability on Limit Cycle Oscillation Behaviour

Modal analysis is a popular approach used in structural dynamic and aeroelastic problems due to its efficiency. The response of a structure is compo
sed of the sum of orthogonal eigenvectors or modeshapes and corresponding modal frequencies. This paper investigates the importance of modeshapes on the aeroelastic response of the Goland wing subject to structural uncertainties. The wing undergoes limit cycle oscillations (LCO) as a result of the inclusion of polynomial stiffness nonlinearities. The LCO computations are performed using a Harmonic Balance approach for speed, the modal properties of the system are extracted from MSC NASTRAN. Variability in both the wing’s structure and the store centre of gravity location is investigated in two cases:- supercritical and subcritical type LCOs. Results show that the LCO behaviour is only sensitive to change in modeshapes when the nature of the modes are changing significantly.

Analysis of Transonic Limit Cycle Oscillations under Uncertainty

For the computation of limit cycle oscillations (LCO) at transonic speeds, CFD is required to capture the nonlinear flow features present. The Harmonic Balance method provides an effective means for the computation of LCOs and this paper exploits its efficiency to investigate the impact of variability (both structural a nd aerodynamic) on the aeroelastic behaviour of a 2 dof aerofoil. A Harmonic Balance inviscid CFD solver is coupled with the structural equations and is validated against time marching analyses. Polynomial chaos expansions are employed for the stochastic investiga tion as a faster alternative to Monte Carlo analysis. Adaptive sampling is employed when discontinuities are present. Uncertainties in aerodynamic parameters are looked at first followed by the inclusion of structural variability. Results show the nonlinear effect of Mach number and it’s interaction with the structural parameters on supercritical LCOs. The bifurcation boundaries are well captured by the polynomial chaos.

Vector bundles on the projective line and finite domination of chain complexes

We present an algebro-geometric approach to a theorem on finite domination of chain complexes over a Laurent polynomial ring. The approach uses extension of chain complexes to sheaves on the projective line, which is governed by a K-theoretical obstruction.

Investigation of Limit Cycle Oscillations Using Aeroelastic-Harmonic Balance Method

This work investigates limit cycle oscillations in the transonic regime. A novel approach to predict Limit Cycle Oscillations using high fidelity analysis is exploited to accelerate calculations. The method used is an Aeroeasltic Harmonic Balance approach, which has been proven to be efficient and able to predict periodic phenomena. The behaviour of limit cycle oscillations is analysed using uncertainty quantification tools based on polynomial chaos expansions. To improve the efficiency of the sampling process for the polynomial-chaos expansions an adaptive sampling procedure is used. These methods are exercised using two problems: a pitch/plunge aerofoil and a delta-wing. Results indicate that Mach n. variability is determinant to the amplitude of the LCO for the 2D test case, whereas for the wing case analysed here, variability in the Mach n. has an almost negligible influence in amplitude variation and the LCO frequency variability has an almost linear relation with Mach number. Further test cases are required to understand the generality of these results.

Prediction of limit cycle oscillations under uncertainty using a Harmonic Balance method

The Harmonic Balance method is an attractive solution for computing periodic responses and can be an alternative to time domain methods, at a reduced computational cost. The current paper investigates using a Harmonic Balance method for simulating limit cycle oscillations under uncertainty. The Harmonic Balance method is used in conjunction with a non-intrusive polynomial-chaos approach to propagate variability and is validated against Monte Carlo analysis. Results show the potential of the approach for a range of nonlinear dynamical systems, including a full wing configuration exhibiting supercritical and subcritical bifurcations, at a fraction of the cost of performing time domain simulations.